SYLLABUS AND HOMEWORK

Mathematics 3001

Analysis 1

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Homework is due in class and must be stapled, with your name on it, to receive credit.

You may find the Mathematics Help Room (MATH 175) to be useful as a meeting point for discussing homework.

 Date Topics covered Reading Homework Assignments Monday August 26 Class Introduction Sec 1-7: Review of background material Read Chapters 1 and 2 Wednesday August 28 Sec 1-7: Review (Cont.) Read Section 8 (especially Theorem 8.10, and work through Example 8.11) Friday August 30 Sec 8: Cardinality Read Section 10 HW 1: Due Friday August 30 Sec 5: 5.1 (a), (d), 5.2 (a-c), 5.3-5.7, 5.8, 5.19-26 Sec 6: 6.2, 6.3, 6.4, 6.8-17 Recommended, but do NOT turn in: Sec 1: 1.2, 1.3, 1.7, 1.8, 1.14 Sec 2: 2.3, 2.5, 2.9, 2.13, 2.14 Sec 3: 3.3, 3.4, 3.5, 3.6 Sec 4: 4.1-5, 4.19, 4.20 Monday September 2 NO CLASS LABOR DAY NO CLASS Wednesday September 4 Sec 10: Natural numbers and induction Read Section 11 (especially familiarize yourself with the axioms of an ordered field, and work through Practice Problems 11.2 and 11.3.) Friday September 6 Sec 11: Ordered Fields HW 2: Due Friday September 6 Sec 7: 7.1-33 odd (except for 7.3, 7.7, 7.9) Sec 8: 8.1, 8.7, 8.16, 8.18 (except for 8.1(d)) Monday September 9 Sec 12: The Completeness Axiom Read Section 12 Wednesday September 11 Construction of the real numbers Read Section 13 Friday September 13 NO CLASS CAMPUS CLOSED NO CLASS Monday September 16 Sec 13: Topology of the real numbers Wednesday September 18 Topological spaces Read Section 14 Friday September 20 Continuous maps, and metric spaces HW 3: Due Friday September 20 Sec 8: 8.19-23 Sec 10: 10.1-16, 10.19, 10.21, 10.22, 10.28. Monday September 23 Sec 14: Compact subsets of the real numbers, compact and connected topological spaces Read Section 16 (you must understand Definition 16.2) Wednesday September 25 Sec 16: Convergence for sequences. Read Section 17 Friday September 27 Sec 16: Convergence for sequences (cont.) HW 4: Due Friday September 27 Sec 7: 7.3, 7.7, 7.9 Sec 8: 8.2, 8.3, 8.9, Sec 11: 11.1, 11.2, 11.3(c)(f)(h)(j)(k), 11.5, 11.7, 11.10, 11.11, 11.12 Sec 12: 12.1, 12.2, 12.6, 12.7 Monday September 30 Homework review Wednesday October 2 Review Friday October 4 MIDTERM I Practice exam .pdf Monday October 7 Sec 17: Limit theorems for sequences Wednesday October 9 Sec 17: Limit theorems for sequences (cont.) Read Section 18 Friday October 11 Sec 18: Monotone sequences and Cauchy sequences Read Section 19 HW 5: Due Friday October 11 Sec 12: 12.10, 12.12, 12.14, 12.15 Sec 13: 13.1, 13.2, 13.3, 13.4, 13.11, 13.15, 13.20 Sec 14: 14.1, 14.2, 14.3, 14.5(a), 14.6 Monday October 14 Sec 18: Monotone sequences and Cauchy sequences (Cont.) Wednesday October 16 Sec 19: Subsequences Friday October 18 Sec 19: Subsequences (cont.) Read Section 20 HW 6: Due Friday October 18 Sec 16: 16.1, 16.2, 16.4, 16.5, 16.6(b)(d)(e), 16.7(a)(f), 16.8(c), 16.11, 16.15 Monday October 21 Sec 20: Limits of functions Wednesday October 23 Sec 20: Limits of functions (cont.) Read Section 21 (work through the proof of Theorem 21.14) Friday October 25 Sec 21: Continuous functions Read Section 22 (work through examples 22.7 and 22.8) Monday October 28 Sec 21: Continuous functions (cont.) HW 7: Due Monday October 28 Sec 17: 17.1, 17.2, 17.3, 17.6, 17.8, 17.15(a) Sec 18: 18.1, 18.2, 18.3(a), 18.4, 18.7, 18.14, 18.15 Wednesday October 30 Sec 22: Properties of continuous functions Read Section 23 Friday November 1 Sec 23: Uniform continuity Read Section 25 (you must understand Definition 25.1, work through Examples 25.2 and 25.4, and do Practice Problem 25.5) HW 8: Due Friday November 8 Sec 19: 19.1, 19.2, 19.5(a)(d)(f), 19.11, 19.12, 19.13 Sec 20: 20.1, 20.2, 20.4, 20.5, 20.7, 20.14, 20.16, 20.18 Monday November  4 Homework review Wednesday November 6 Review Friday November 8 MIDTERM II Practice exam .pdf Monday November 11 Sec 25: The Derivative Wednesday November 13 Sec 25: The Derivative (cont.) Read Section 26 (especially Example 26.4 and do Practice Problem 26.5) Friday November 15 Sec 26: The Mean Value Theorem Read Section 29 HW 9: Due Friday November 15 Sec 21: 21.1, 21.2, 21.3, 21.6(c)(d)(f), 21.11 Sec 22: 22.1, 22.2, 22.3(a)(b)(e), 22.5, 22.7, 22.13 Monday November 18 Sec 29: The Riemann Integral Wednesday November 20 Sec 29: The Riemann Integral (cont.) Read Section 30 Friday November 22 Sec 30: Properties of the Riemann Integral Read Section 31 HW 10: Due Friday November 22 Sec 23: 23.1, 23.2, 23.3(d)(e), 23.5 Sec 25: 25.1, 25.2, 25.5 Monday November 25 - Friday November 29 NO CLASS THANKSGIVING BREAK NO CLASS Monday December 2 Sec 31: The Fundamental Theorem of Calculus Wednesday December 4 Further topics Friday December 6 Further topics HW 11: Due Friday December 6 Sec 25: 25.6, 25.7(d), 25.8, 25.11, 25.15 Sec 26: 26.1, 26.2, 26.6, 26.10, 26.11, 26.15 Monday December 9 Further topics Wednesday December 11 Homework review Friday December 13 Review HW 12: Due Friday December 13 (Not for credit, do not turn in) Sec 29: 29.1, 29.2, 29.5, 29.7, 29.8, 29.9, 29.11, 29.13, 29.16 Sec 30: 30.1, 30.2, 30.3, 30.9, 30.11, 30.12, 30.15, 30.21 Sec 31: 31.1, 31.2, 31.4, 31.5, 31.12, 31.13 Saturday December 14 FINAL EXAM DUAN G131 7:30-10:00 PM FINAL EXAM Practice exam .pdf

For those of you typing up your homework, you may want to consider learning to use LaTex.  If you have a mac, one possible easy way to get started is with texshop.  If you are using linux, there are a number of other possible ways to go, using emacs, ghostview, etc.  If you are using windows, you're on your own, but I'm sure there's something online.  Here is a sample homework file to use: (the .tex file, the .bib file, and the .pdf file).  It is probably easiest to just look at the .tex file, and start to experiment.  There is also the (Not so) short introduction to latex, which will answer most of your questions (although typing your question into your favorite search engine will probably work well, too).  You may also want to try http://scribtex.com/ for a cloud version.